Structured scale dependence in the Lyapunov exponent of a Boolean chaotic map

Abstract

We report on structures in a scale-dependent Lyapunov exponent of an experimental chaotic map that arise due to discontinuities in the map. The chaos is realized in an autonomous Boolean network which is constructed using asynchronous logic gates to form a map operator that outputs an unclocked pulse-train of varying widths. The map operator executes pulse-width stretching and folding and the operator's output is fed back to its input to continuously iterate the map. Using a simple model, we show that the structured scale-dependence in the system's Lyapunov exponent is the result of the discrete logic elements in the map operator's stretching function.

Long-Range Pulse Interactions in Unclocked FPGAs

“…Recent applications include timeto-digital converters (TDCs) [1], [2], physically unclonable functions (PUFs) [3]- [7], true random number generators (TRNGs) [8]- [11], and reservoir computers [12]- [14]. In many of these designs, cascaded logic elements (often an even number of inverters or NOT-gates [15], [16]) are used to approximate ideal delays for logic levels and switching times. However, as software-defined delays in FPGAs continue to be used in designs, it is important to explore and understand non-ideal behaviors, particularly those that may occur on unexpected timescales.…”